Abstract

In this review article, we explore several recent advances in
the quantitative modeling of financial markets. We begin with the
Efficient Markets Hypothesis and describe how this controversial idea
has stimulated a number of new directions of research, some focusing on
more elaborate mathematical models that are capable of rationalizing
the empirical facts, others taking a completely different tack in
rejecting rationality altogether. One of the most promising directions
is to view financial markets from a biological perspective and,
specifically, within an evolutionary framework in which markets,
instruments, institutions, and investors interact and evolve
dynamically according to the “law” of economic selection. Under
this view, financial agents compete and adapt, but they do not
necessarily do so in an optimal fashion. Evolutionary and ecological
models of financial markets is truly a new frontier whose exploration
has just begun.

If, in January, 1926, an individual invested $1 in one-month
U.S. Treasury bills—one of the safest securities in the world—and
continued reinvesting the proceeds month by month until December, 1996,
the original investment would have grown to $14. If, on the other hand,
an individual invested $1 in the S&P 500—a much riskier
investment—over the same 71-year period, this investment would have
grown to $1,370, a considerably larger sum. Now suppose that, each
month, an individual were able to divine in advance which of these two
investments would yield a higher return for that month and took
advantage of this information by switching the running total of his
initial $1 investment into the higher-yielding asset. What would a $1
investment in such a “perfect foresight” investment strategy
become by December 1996?

The startling answer is $2,296,183,456, more than two billion
dollars!§ Despite the fact that perfect foresight in financial
markets is impossible, this example suggests that even a modest ability
to forecast financial asset returns may be handsomely rewarded. Of
course, there are considerable risks involved. As recent financial
calamities such as that of Long Term Capital Management have made very
clear, it is also possible to lose very large sums of money. Financial
markets are very difficult to predict; otherwise, we would all be rich.
One of the central questions, indeed, perhaps the most central question
in finance, is, “Under what circumstances is prediction possible at
all?”

In this review article, we explore this issue in light of recent
advances in the quantitative modeling of financial markets. The potent
combination of breakthroughs in financial technology and computational
speed and efficiency is creating an exciting renaissance in financial
research, both inside and outside the halls of academia. It is
impossible for us to provide a complete survey of these developments
here; instead, we focus on the beginnings of a new research direction
that the emerging fields of computational finance and financial
engineering may be heading toward—evolutionary and ecological models
of financial markets—and how these new perspectives may be changing
fundamental views about market prediction.

Our starting point is the “Efficient Markets Hypothesis”
(EMH), a powerful idea that can be traced back to Paul Samuelson (1),
whose contribution is neatly summarized by the title of his article:
“Proof that Properly Anticipated Prices Fluctuate Randomly.” In
an informationally efficient market, price changes must be
unforecastable if they are properly anticipated, i.e., if they fully
incorporate the expectations and information of all market
participants.

This concept of informational efficiency has a wonderfully
counterintuitive and seemingly contradictory flavor to it: the more
efficient the market, the more random the sequence of price changes
generated by such a market must be, and the most efficient market of
all is one in which price changes are completely random and
unpredictable. This, of course, is not an accident of nature but is the
direct outcome of many active participants attempting to profit from
their information. Unable to curtail their greed, an army of investors
aggressively pounce on even the smallest informational advantages at
their disposal, and, in doing so, they incorporate their information
into market prices and quickly eliminate the profit opportunities that
gave rise to their actions. If this occurs instantaneously, which it
must in an idealized world of “frictionless” markets and costless
trading, then prices must always fully reflect all available
information, and no profits can be garnered from information-based
trading (because such profits have already been
captured).

But one of the central tenets of modern financial economics is
the necessity of some trade-off between risk and expected return. If a
security’s expected price change is positive, it may be just the
reward needed to attract investors to hold the asset and bear the
corresponding risks. Indeed, if an investor is sufficiently risk
averse, he might gladly pay to avoid holding a security that has
unforecastable returns. In such a world, prices do not need to be
perfectly random, even if markets are operating efficiently and
rationally.

Indeed, several statistical studies have made it clear that
prices are, in fact, not completely random (see, for example, ref. 2).
Economists disagree on whether this represents a violation of efficient
markets. Similarly, the sustained profits of some investment companies
and certain high-profile portfolio managers seem to challenge the very
foundations of market rationality and efficiency. Are they just lucky?
Are they merely receiving appropriate compensation for risk? Or are
markets simply inefficient? Such questions have proved to be difficult
to answer and remain controversial.

One of the reasons for this state of affairs is the fact that the
EMH, by itself, is not a well posed and empirically refutable
hypothesis. To make it operational, one must specify additional
structure: e.g., investors’ preferences, information structure, etc.
But then a test of the EMH becomes a test of several auxiliary
hypotheses as well, and a rejection of such a joint hypothesis tells us
little about which aspect of the joint hypothesis is inconsistent with
the data. Moreover, new statistical tests designed to distinguish among
them will no doubt require auxiliary hypotheses of their own that, in
turn, may be questioned. The hypothesis that investors are fully
rational agents that instantaneously and correctly process all
available information is clearly unrealistic—rationality is difficult
to define, human behavior is often unpredictable, information can be
difficult to interpret, technology and institutions change constantly,
and there are significant “frictional” costs to gathering and
processing information and transacting. But how can we take all of the
complexities of the real world into account?

One new direction is to treat the EMH as an idealization that
provides a useful reference point. For example, one can ask about the
relative efficiency of markets with respect to each other: e.g.,
futures vs. spot markets, auction vs. dealer markets, etc. The
advantages of the concept of relative efficiency, as opposed to the
all-or-nothing notion of absolute efficiency, are easy to spot by way
of an analogy to the concept of efficiency as used in physics. Heat
engines can be given an efficiency rating based on the fraction of
available energy that they convert into useful work. A refrigerator
with an efficiency of 40% might be considered quite good, and a buyer
would prefer this to one with an efficiency of only 35%. No one would
ever expect 100% efficiency. The best measure of the relative
efficiency of financial markets, relative to each other, is a topic on
the frontiers of research in finance.

Another point of view is to extend the definition of efficient
markets so that consistent profits are possible to those who acquire a
competitive advantage. The motivation for this becomes apparent from
applying the classical version of the EMH to a nonfinancial context,
such as a biotechnology firm attempting to develop a vaccine for the
AIDS virus. If the market for biotechnology is efficient in the
classical EMH sense, such a vaccine can never be developed—if it
could, someone would have already done it! This is clearly an absurd
conclusion because it ignores the challenges and gestation lags of
research and development in biotechnology. If a pharmaceutical company
does succeed in developing such a vaccine, the profits earned might be
measured in the billions of dollars—would this be considered
“excess” profits or simply an appropriate economic reward for
competence and innovation? Financial markets should not be different in
principle, only in degree. The profits that accrue to an investment
professional need not be a market inefficiency but may simply be the
fair reward for unusual skill, extraordinary effort, or for
breakthroughs in financial technology.

What, then, can we conclude about the EMH? Amazingly, there is
still no consensus among financial economists. Despite the many
advances in the statistical analysis, databases, and theoretical models
surrounding the EMH, the main effect has been to harden the resolve of
the proponents on each side.

However, the controversy surrounding the EMH has stimulated a
number of new directions of research, some focusing on more elaborate
mathematical models that are capable of rationalizing the empirical
facts, others taking a completely different tack in rejecting
rationality altogether. We think one of the most promising directions
is to view financial markets from a biological perspective and,
specifically, within an evolutionary framework in which markets,
instruments, institutions, and investors interact and evolve
dynamically according to the “law” of economic selection. Under
this view, financial agents compete and adapt, but they do not
necessarily do so in an optimal fashion.

The desire to build financial theories based on more realistic
assumptions has led to several new strands of literature, including
psychological approaches to risk-taking behavior (3–5), evolutionary
game theory (6), and agent-based modeling of financial markets (ref. 7;
N. Chan, B. LeBaron, A.L., and T. Poggio, unpublished work). Although
substantially different in methods and style, these emerging subfields
are all directed at new interpretations of the EMH. In particular,
psychological models of financial markets focus on the manner in which
human psychology influences the economic decision-making process as an
explanation of apparent departures from rationality. Evolutionary game
theory studies the evolution and steady-state equilibria of populations
of competing strategies in highly idealized settings. Agent-based
models are meant to capture complex learning behavior and dynamics in
financial markets by using more realistic markets, strategies, and
information structures.

For example, in one agent-based model of the financial markets
(J.D.F., unpublished work), the market is modeled by using a
nonequilibrium market mechanism whose simplicity makes it possible to
obtain analytic results while maintaining a plausible degree of
realism. Market participants are treated as computational entities that
employ strategies based on limited information. Through their
(sometimes suboptimal) actions, they make profits or losses. Profitable
strategies accumulate capital with the passage of time, and
unprofitable strategies lose money and may eventually disappear. A
financial market can thus be viewed as a coevolving ecology of trading
strategies. The strategy is analogous to a biological species, and the
total capital deployed by agents following a given strategy is
analogous to the population of that species. The creation of new
strategies may alter the profitability of preexisting strategies, in
some cases replacing them or driving them extinct.

Although agent-based models are still in their infancy, the
simulations and related theory have already demonstrated an ability to
understand many aspects of financial markets. Several studies indicate
that, as the population of strategies evolve, the market tends to
become more efficient, but this is far from the perfect efficiency of
the classical EMH. Prices fluctuate in time with internal dynamics
caused by the interaction of diverse trading strategies. Prices do not
necessarily reflect “true values”; if we view the market as a
machine whose job is to set prices properly, the inefficiency of this
machine can be substantial. Patterns in the price tend to disappear as
agents evolve profitable strategies to exploit them, but this occurs
only over an extended period of time, during which substantial profits
may be accumulated and new patterns may appear.

Thomas Malthus and Adam Smith—two of the forefathers of modern
economics—were both cited by Darwin as inspirations for the principle
of natural selection, and analogies between economics and biology have
been discussed for more than a century. However, a quantitative
foundation for this approach has been slow to develop. Recent research
in finance suggests that this is about to change (5). Although there
are obvious differences between evolution in biological systems and
evolution in financial systems, there are also many similarities. The
theory of evolution may prove to be as powerful an idea in finance as
it has been in biology. There is no lack of quantitative data, and
there are many opportunities for biological principles to be applied to
financial interactions—after all, financial institutions are uniquely
human inventions that provide an adaptive advantage to our species.
This is truly a new frontier whose exploration has just begun.

Acknowledgments

We thank the participants of the National Academy of
Sciences 1998 Frontiers of Science Symposium for valuable discussions
and comments. This research was partially supported by the
Massachusetts Institute of Technology Laboratory for Financial
Engineering and the National Science Foundation (Grant SBR-9709976).

Footnotes

↵† To whom reprint requests should be addressed. E-mail:
jdf{at}santafe.edu.

This paper is a summary of a session presented at the tenth
annual symposium on Frontiers of Science, held November 19–21,
1998, at the Arnold and Mabel Beckman Center of the National Academies
of Sciences and Engineering in Irvine, CA.

↵§ We are grateful to Bob Merton (Harvard University
Business School) for this example.

Environmental factors, not genes constitute most disease risk. Myriad approaches are attempting to use the latest science and technology to more clearly reveal the complex mix of pollutants that contribute.

Blood-sucking sand flies from disparate global regions have a predilection for feeding on the marijuana plant (Cannabis sativa), and the findings hint at a potential avenue for controlling sand flies, which can transmit leishmaniasis.